If you were a celebrity who came on "Late Night" (his 1980s NBC show) or "The Late Show" (his CBS successor) simply to chat about your new movie or album or TV show, good luck to you. Dave -- he was always "Dave" -- might be interested, but more likely he was bored or cranky. He much preferred the Steve Martins or Bill Murrays of the world who would use their spot to do something silly.

Memorable 'Late Show' moments 20 photos

Memorable 'Late Show' moments20 photos

Memorable 'Late Show' moments – Even when CBS' "Late Show with David Letterman" veers into awkward, uncomfortable territory for the guest -- as it often does -- Letterman never loses his cool. In fact, the opposite happens: The show only gets better. Now, after more than 30 years in the business, Letterman has mastered the art of pressing just the right buttons to ensure great TV.

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Memorable 'Late Show' moments20 photos

Memorable 'Late Show' moments – Any moment with legend Johnny Carson and legend-in-the-making Letterman was destined to be a classic, but Carson's appearance on the "Late Show" in May 1994 is the most memorable. The former "Tonight Show" host opted to make his last TV showing with Letterman, who appropriately handed over his desk chair to his idol.

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Memorable 'Late Show' moments20 photos

Tribute to Johnny Carson – After Johnny Carson died in January 2005, David Letterman paid tribute to him in the best way he knew: by turning over his entire monologue to the celebrated comedian and TV personality, composing it of jokes Carson had written.

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Memorable 'Late Show' moments20 photos

Madonna's F-bombs – In March 1994, Madonna severely tested Letterman's mettle in an exchange that's become a standout late night moment. Letterman introduced Madge as a top-selling pop star who'd slept with some of the biggest names in the industry, which prompted Madonna to go off a very profane deep end. At last count, somewhere around 13 F-bombs were dropped over the course of the interview.

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Memorable 'Late Show' moments20 photos

Drew Barrymore flashes Dave – When Drew Barrymore showed up on "Letterman" in 1995, she came bearing gifts -- of a sort. The then-20-year-old actress was a ball of "good energy," and when talk turned to her interest in "nude performance dance," Letterman of course had to get a preview -- complete with flashing. It was his birthday, after all.

First broadcast after 9/11 – Letterman's first show after the September 11 attacks was an understandably subdued and emotional episode. The monologue was skipped in favor of honoring those lost in the attack. Dan Rather was one of the night's guests, and he memorably couldn't hold back tears as he recited "America the Beautiful."

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Memorable 'Late Show' moments20 photos

Honoring Warren Zevon – In the fall of 2002, Letterman showed his graciousness and tender heart when he dedicated an entire episode to the terminally ill Warren Zevon in a celebration of his music. The singer-songwriter passed away the following year.

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Memorable 'Late Show' moments20 photos

McCartney performs – Musician Paul McCartney took over the marquee of the Ed Sullivan Theater, where the Beatles made big news in 1964, to performs for the '"Late Show" on July 15, 2009.

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Memorable 'Late Show' moments20 photos

Dave and Oprah bury the hatchet – It had been 16 years since Oprah Winfrey last set foot on "Letterman" when she finally returned in December 2005. The episode of course brought in monster ratings, as it appeared that the two were making up. The irony was that neither truly knew -- or at least would admit on TV -- what caused their supposed "feud," or if there was ever a tiff in the first place.

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Memorable 'Late Show' moments20 photos

Michael Richards' mea culpa – When you need to make a massive apology, it makes sense to turn to the well-respected Letterman to help you out. That's what "Seinfeld's" Michael Richards ended up doing in November 2006, with help from Letterman's guest of the night, Jerry Seinfeld. Richards, however, wasn't in the studio -- he made his apology via satellite after coming under fire for using the N-word during a tirade at a comedy club. "Awkward" doesn't begin to describe the appearance.

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Memorable 'Late Show' moments20 photos

Dave and Bill O'Reilly call a truce – Before Bill O'Reilly and David Letterman found a reason to high-five one another in 2011, they'd had a war of words while taping "Late Show" in 2006. The conversation was about the Iraq War, and the debate became so agitated that the light-hearted comments turned into terse insults.

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Memorable 'Late Show' moments20 photos

Paris Hilton gets grilled – Paris Hilton braved seeing Letterman again in 2008 even after he upset her during her 2007 interview. The late night host grilled her about her jail time to the point that she said she was "sad" she'd even come on the show. The following year, Letterman acknowledged how tough he'd been on the celebutante and made nice.

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Memorable 'Late Show' moments20 photos

John McCain in the hot seat – After initially trying to skip out on Letterman's show in 2008, John McCain finally made it into the hot seat that October. The politician was faced with chatting up a man who roasted him for his cancellation in an earlier monologue. Both moments were deliciously squirmy TV.

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Memorable 'Late Show' moments20 photos

Joaquin Phoenix's strange act – Watching Joaquin Phoenix appear on "Letterman" in 2009 was like watching a train wreck -- it was so hard to watch, but you just couldn't look away. Phoenix had drastically altered his appearance and behaved strangely, as Letterman tried to figure out how to navigate the puzzle before him. It was all an act, though, and Phoenix returned to the show in 2010 to apologize.

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Memorable 'Late Show' moments20 photos

Dave's shocking confession – In October 2009, Letterman made a stunning admission live on the air when he told his audience that he'd had sexual relationships with female members of his staff, and that someone had been attempting to blackmail him as a result. The following Monday, he used his show to offer a "heartfelt" apology to his wife and to his female staffers.

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Memorable 'Late Show' moments20 photos

Richard Simmons goes up in smoke – Richard Simmons and David Letterman have a wonderfully antagonistic friendship, and out of the many times the fitness king has appeared on the program, it's hard to pick a favorite. This moment from 2009, when Simmons and Letterman bickered over how to use a food steamer just before it burst into flames, is the kind of late night gold that other hosts dream about.

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Memorable 'Late Show' moments20 photos

Dave and Jay Leno team up – Letterman isn't above poking some friendly fun at his rival, Jay Leno, and in the disastrous NBC late night wars of 2010, Letterman kicked it up a notch. But, we assume, it was all in good fun -- Letterman still joined Oprah Winfrey and Leno in a "Late Show" promo during the Super Bowl that year, an ad that was said to be Letterman's idea.

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Memorable 'Late Show' moments20 photos

Lindsay Lohan gets emotional – Prior to her court-mandated stint in rehab, Lindsay Lohan gave an emotional but also surprisingly endearing and transparent interview. Letterman, of course, didn't take the easy route and asked pointed, frank questions. Although he led her down a road that ended in tears, the host commended Lohan when it was done: "We never thought we'd see you again, honestly, because of the jokes and stuff," he told her. "But you have enough spine, enough sense of yourself, enough poise to come out here and talk to me."

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Memorable 'Late Show' moments20 photos

Cher keeps Dave on his toes – Cher and Letterman have a storied past, as the singer seems to have a unique ability to confound the comedian. Once in 1996 she told him he looked like "s---," and generally gave him a hard time. However, the singer has appeared on his show several times since, including in 2013, when she gave him a big hug after performing a song off her latest album.

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EXPAND GALLERY

It was a comedic style that never really captured Middle America -- for most of their 20-year rivalry, Jay Leno's ratings were much higher than Letterman's -- but influenced a generation of comedians and comedy writers.

"The Simpsons," Ben Stiller, Conan O'Brien, Jimmy Kimmel, any comedian or comedy that used irony, silliness, absurdity and a little bit of antagonism as their stock in trade -- Dave made network television, previously an irony-free zone, safe for all of them. (There was more than a little Letterman in Garry Shandling's curdled, insecure faux talk-show host, Larry Sanders.)

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"He did the thing that everyone's tried to do since and has never done, which is to take the talk-show form and redo it," Jerry Seinfeld, an early Letterman guest, told Rolling Stone in 2011. "The mindset was, 'We're tired of pretending there are no cue cards and no cameras and nothing's rehearsed. It's late, and we're going to take over this little piece of territory and do our own thing.' Now that mindset is everywhere."

Reveling in friction

At its best, Letterman's late-night show was unpredictable, particularly in the 1980s, when it was all new. He once used pictures from an old Sears catalog over the opening credits. He did a "360-degree show," letting the camera rotate all the way around during the course of the hour. (At the half-hour mark, Letterman was upside-down.)

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His interviews -- the "talk" of talk shows -- were often deliberately devoid of content. Sometimes he used his guests for comedy bits, as when Steve Martin, allegedly on the set to promote a movie, deplored Letterman's questions and then had the Late Show Gospel Choir launch into a gospel song about himself.

Other times they were, shall we say, antagonistic. Perhaps the most famous example was an appearance by actor Crispin Glover ("Back to the Future") in 1987. At one point, Glover got up to demonstrate a roundhouse kick. Letterman went to a commercial break. When he returned, Glover was gone.

Of course, Letterman reveled in friction. Both Cher and Madonna had tetchy interviews with the host. He made much of an alleged feud with Oprah Winfrey. During the "Late Night" days, he booked people like Brother Theodore or "American Splendor" cartoonist Harvey Pekar: types who were the very antithesis of talk-show guests, types who made audiences uncomfortable.

Letterman grew up a bit when he went to CBS in 1993. With NBC, he wore blazers and sneakers, very much the impish college boy. Suddenly he was in nice suits and shined shoes. The guests became more of the A-list variety, though Dave was still the type to make room for a musician like Warren Zevon, a personal favorite who would never have passed muster on Leno's "Tonight."

But it probably says something that Letterman's most striking moments of recent years came when he dropped the ironic pose and spoke from the heart. These moments -- paying tribute to mentor Johnny Carson, thanking his heart surgeons, talking about his son, confessing to an affair -- made the very private host seem a little more approachable.

Given some of the stories about Letterman's self-loathing that his former partner and onetime head writer, Merrill Markoe, has told over the years, he probably hated that.

And there's something a little awkward about Letterman, the King of Absurdity, still presiding over his anti-talk show circus at the age of 67. (He turns 68 in April.) It's not that he can't pull it off; it's that he's been doing it for so long that his original college student audience now has children (and grandchildren!) of their own. They have so many more options, and Dave is now one of many.

Stephen Colbert, who created his own kind of looking-glass show, will take over this year. No doubt he'll bring his own absurdity to the role.